Gambler's fallacy

The incorrect belief that the likelihood of a random event can be affected by or predicted from other, independent events.

Example

Form

Treatment

If for example 6 consequtive sixes have been thrown. People know from observation this is a very rare event. throwing 7 sixes consequtively is even rarer. Therefore the probability of the next number being thrown is less than 1 in 6. This is a fallacy. If the dice is random the probability remains 1 in 6. Previous events don't change the randomness of the current event. This can be tested experimentally and has been.